A necessary and sufficient condition for rationalizability in a quasi-linear context |
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| Affiliation: | 1. Ecole Polytechnique, 75230 Paris, France;2. Université Paris IX-Dauphine, Paris, France;1. Baruch College, City University of New York, United States of America;2. Royal Holloway, University of London, United Kingdom of Great Britain and Northern Ireland;3. School of Economics, Tel Aviv University, Israel;4. Department of Economics, New York University, United States of America;1. Department of Economics, University of Montréal, Canada;2. Department of Economics, University of Bonn, Germany |
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| Abstract: | The aim of this note is to give a simple characterization of the rationalizability of decision rules (or action profiles). The necessary and sufficient condition we obtain suggests interesting analogies between the Implementation Problem and Revealed Preference Theory. Two particular cases are examined: - 1.(a) The one-dimensional context, which shows that our condition is a generalization of the monotonicity condition of Spence-Mirrlees,
- 2.(b) The linear set-up, which shows that rationalizability in multiple dimension requires more than monotonicity: it implies also symmetry conditions which are translated by Partial Differential Equations (analogue in this context of Slutsky equations for Revealed Preference Theory).
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